The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen-like ion. The atomic number `Z` of hydrogen-like ion is

Options

A. 3
B. 4
C. 1
D. 2

Answer

D

Explanation

For hydrogen atom
`1/lambda=R(1/1^2-1/2^2)`
For the given hydrogen-like ion
`1/lambda=RZ^2(1/2^2-1/4^2)`
`rArr (1/1^2-1/2^2)=Z^2(1/2^2-1/4^2)`
`rArr` Z=2